New phenomena appear in the course of quantization,
in particular anomalies are present [1]}.
In vector gauge theories like massless QED they describe physical phenomena but in
a chiral gauge theory they break precisely the symmetry
on which such theories are based, producing an inconsistency, see e.g. [2]}, [3]}.
The Standard Electroweak theory is a chiral gauge theory which has
anomalies for generic values of the parameters, manifesting in the breaking of conservation of the
hypercharge current \(j_\mu ^B\)  for generic values of \(Y_{i,s}\) .
This phenomenon is present already considering \(B_\mu , W_\mu \)  as classical background fields:
the average of hypercharge current \(j_\mu ^B\)  can be written as a series expansion in the external fields whose second order coefficients are
\(<j^B_\mu j^B_\nu j^B_\rho >_0\) , or
\(<j^B_\mu j^W_\nu j^W_\rho >_0\) , where \(<>_0\)  is the average with respect
to non-interacting fermions. The outcome is that
generically
\(p_\mu <\widehat{j}^B_\mu \widehat{j}^B_\nu \widehat{j}^B_\rho >_0\) , or
\(p_\mu <\widehat{j}^B_\mu \widehat{j}^W_\nu \widehat{j}^W_\rho >_0\)  are non vanishing except if the hypercharges
verify
the anomaly cancellation conditions [4]}
\(&&Y^L_e+ Y^L_\nu +3 Y^L_u+ 3 Y^L_d =0\nonumber \hfill &&(Y^L_e)^3+(Y^L_\varepsilon )^3+3 (Y^L_u)^3+3(Y^L_d)^3-(Y^R_e)^3-(Y^R_\varepsilon )^3-3 (Y^R_u)^3-3(Y^R_d)^3=0\) 
